# Real Analysis, differentiation

Solved: Real Analysis, differentiation

## Homework Statement

If g is differentiable and g(x+y)=g(x)(g(y) find g(0) and show g'(x)=g'(0)g(x)

## The Attempt at a Solution

I solved g(0)=1

and

I got as far as

$$g'(x)=\lim_{\substack{x\rightarrow 0}}g(x) \frac{g(h)-1}{h}$$

but now I am stuck.

Last edited:

Never mind... Just did g'(0) and plug in...

HallsofIvy
$$g'(x)= \lim_{\substack{h\rightarrow 0}}g(x)\frac{g(h)- 1}{h}$$
$$g'(x)= g(x)\left(\lim_{\substack{h\rightarrow 0}}\frac{g(h)-1}{h}\right)$$